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1.  Numerical investigations of MRI RF field induced heating for external fixation devices 
The magnetic resonance imaging (MRI) radio frequency (RF) field induced heating on external fixation devices can be very high in the vicinity of device screws. Such induced RF heating is related to device constructs, device placements, as well as the device insertion depth into human subjects. In this study, computational modeling is performed to determine factors associated with such induced heating.
Numerical modeling, based on the finite-difference time-domain (FDTD) method, is used to evaluate the temperature rises near external device screw tips inside the ASTM phantom for both 1.5-T and 3-T MRI systems. The modeling approach consists of 1) the development of RF coils for 1.5-T and 3-T, 2) the electromagnetic simulations of energy deposition near the screw tips of external fixation devices, and 3) the thermal simulations of temperature rises near the tips of these devices.
It is found that changing insertion depth and screw spacing could largely affect the heating of these devices. In 1.5-T MRI system, smaller insertion depth and larger pin spacing will lead to higher temperature rise. However, for 3-T MRI system, the relation is not very clear when insertion depth is larger than 5 cm or when pin spacing became larger than 20 cm. The effect of connection bar material on device heating is also studied and the heating mechanism of the device is analysed.
Numerical simulation is used to study RF heating for external fixation devices in both 1.5-T and 3-T MRI coils. Typically, shallower insertion depth and larger pin spacing with conductive bar lead to higher RF heating. The heating mechanism is explained using induced current along the device and power decay inside ASTM phantom.
PMCID: PMC3610272  PMID: 23394173
RF heating; External fixation device; MRI compatible devices
2.  Resonant Mode Reduction in Radiofrequency Volume Coils for Ultrahigh Field Magnetic Resonance Imaging 
Materials  2011;4(8):1333-1344.
In a multimodal volume coil, only one mode can generate homogeneous Radiofrequency (RF) field for Magnetic Resonance Imaging. The existence of other modes may increase the volume coil design difficulties and potentially decreases coil performance. In this study, we introduce common-mode resonator technique to high and ultrahigh field volume coil designs to reduce the resonant mode while maintain the homogeneity of the RF field. To investigate the design method, the common-mode resonator was realized by using a microstrip line which was split along the central to become a pair of parallel transmission lines within which common-mode currents exist. Eight common-mode resonators were placed equidistantly along the circumference of a low loss dielectric cylinder to form a volume coil. Theoretical analysis and comparison between the 16-strut common-mode volume coil and a conventional 16-strut volume coil in terms of RF field homogeneity and efficiency was performed using Finite-Difference Time-Domain (FDTD) method at 298.2 MHz. MR imaging experiments were performed by using a prototype of the common-mode volume coil on a whole body 7 Tesla scanner. FDTD simulation results showed the reduced number of resonant modes of the common-mode volume coil over the conventional volume coil, while the RF field homogeneity of the two type volume coils was kept at the same level. MR imaging of a water phantom and a kiwi fruit showing the feasibility of the proposed method for simplifying the volume coil design is also presented.
PMCID: PMC3212035  PMID: 22081791
Finite-Difference Time-Domain; common-mode; microstrip; Magnetic Resonance Imaging; high field
3.  SAR calculations from 20 MHz to 6 GHz in the University of Florida newborn voxel phantom and their implications for dosimetry 
Physics in medicine and biology  2010;55(5):1519-1530.
This paper presents Finite-Difference Time-Domain, FDTD calculations of SAR in the University of Florida newborn female model. The newborn model is based upon a surface representation of the organs of the body, using non-uniform rational B-spline surfaces, NURBS. The surface model can then be converted into voxels at any resolution required. This flexibility allows the preparation of voxel models at 2-, 1- and 0.5 mm to investigate the effect of resolution on dispersion and the choice of SAR averaging algorithms as the frequency increases up to 6 GHz. The added advantage of the newborn model is that it is relatively small and so FDTD calculations can be made tractable at the very fine resolution of 0.5 mm. A comparison is made between the calculated external electric fields required to produce the basic restriction on whole-body averaged SAR and the ICNIRP reference levels for public exposure. At 250 MHz, the whole body resonance, the ICNIRP reference level does not provide a conservative estimate of the whole-body averaged SAR restriction. The reference level is also breached in the range 700 to 2450 MHz by all of the irradiation geometries considered.
PMCID: PMC3927542  PMID: 20157229
4.  Magnetic nanoparticle density mapping from the magnetically induced displacement data: a simulation study 
Magnetic nanoparticles are gaining great roles in biomedical applications as targeted drug delivery agents or targeted imaging contrast agents. In the magnetic nanoparticle applications, quantification of the nanoparticle density deposited in a specified region is of great importance for evaluating the delivery of the drugs or the contrast agents to the targeted tissues. We introduce a method for estimating the nanoparticle density from the displacement of tissues caused by the external magnetic field.
We can exert magnetic force to the magnetic nanoparticles residing in a living subject by applying magnetic gradient field to them. The nanoparticles under the external magnetic field then exert force to the nearby tissues causing displacement of the tissues. The displacement field induced by the nanoparticles under the external magnetic field is governed by the Navier's equation. We use an approximation method to get the inverse solution of the Navier's equation which represents the magnetic nanoparticle density map when the magnetic nanoparticles are mechanically coupled with the surrounding tissues. To produce the external magnetic field inside a living subject, we propose a coil configuration, the Helmholtz and Maxwell coil pair, that is capable of generating uniform magnetic gradient field. We have estimated the coil currents that can induce measurable displacement in soft tissues through finite element method (FEM) analysis.
From the displacement data obtained from FEM analysis of a soft-tissue-mimicking phantom, we have calculated nanoparticle density maps. We obtained the magnetic nanoparticle density maps by approximating the Navier's equation to the Laplacian of the displacement field. The calculated density maps match well to the original density maps, but with some halo artifacts around the high density area. To induce measurable displacement in the living tissues with the proposed coil configuration, we need to apply the coil currents as big as 104A.
We can obtain magnetic nanoparticle maps from the magnetically induced displacement data by approximating the Navier's equation under the assumption of uniform-gradient of the external magnetic field. However, developing a coil driving system with the capacity of up to 104A should be a great technical challenge.
PMCID: PMC3310781  PMID: 22394477
5.  Electromagnetic Wave Propagation in Body Area Networks Using the Finite-Difference-Time-Domain Method 
Sensors (Basel, Switzerland)  2012;12(7):9862-9883.
A rigorous full-wave solution, via the Finite-Difference-Time-Domain (FDTD) method, is performed in an attempt to obtain realistic communication channel models for on-body wireless transmission in Body-Area-Networks (BANs), which are local data networks using the human body as a propagation medium. The problem of modeling the coupling between body mounted antennas is often not amenable to attack by hybrid techniques owing to the complex nature of the human body. For instance, the time-domain Green's function approach becomes more involved when the antennas are not conformal. Furthermore, the human body is irregular in shape and has dispersion properties that are unique. One consequence of this is that we must resort to modeling the antenna network mounted on the body in its entirety, and the number of degrees of freedom (DoFs) can be on the order of billions. Even so, this type of problem can still be modeled by employing a parallel version of the FDTD algorithm running on a cluster. Lastly, we note that the results of rigorous simulation of BANs can serve as benchmarks for comparison with the abundance of measurement data.
PMCID: PMC3435949  PMID: 23012575
Body Area Networks; FDTD; conformal; numerical phantoms; Cole-Cole model; recursive convolution method; mutual coupling
6.  The Revised Electromagnetic Fields Directive and Worker Exposure in Environments With High Magnetic Flux Densities 
Annals of Occupational Hygiene  2014;58(5):529-541.
Some of the strongest electromagnetic fields (EMF) are found in the workplace. A European Directive sets limits to workers’ exposure to EMF. This review summarizes its origin and contents and compares magnetic field exposure levels in high-risk workplaces with the limits set in the revised Directive. Pubmed, Scopus, grey literature databases, and websites of organizations involved in occupational exposure measurements were searched. The focus was on EMF with frequencies up to 10 MHz, which can cause stimulation of the nervous system. Selected studies had to provide individual maximum exposure levels at the workplace, either in terms of the external magnetic field strength or flux density or as induced electric field strength or current density. Indicative action levels and the corresponding exposure limit values for magnetic fields in the revised European Directive will be higher than those in the previous version. Nevertheless, magnetic flux densities in excess of the action levels for peripheral nerve stimulation are reported for workers involved in welding, induction heating, transcranial magnetic stimulation, and magnetic resonance imaging (MRI). The corresponding health effects exposure limit values for the electric fields in the worker’s body can be exceeded for welding and MRI, but calculations for induction heating and transcranial magnetic stimulation are lacking. Since the revised European Directive conditionally exempts MRI-related activities from the exposure limits, measures to reduce exposure may be necessary for welding, induction heating, and transcranial nerve stimulation. Since such measures can be complicated, there is a clear need for exposure databases for different workplace scenarios with significant EMF exposure and guidance on good practices.
PMCID: PMC4305112  PMID: 24557933
electromagnetic fields; legislation; occupational exposure; peripheral nervous system
7.  Spatial and Temporal Controlled Tissue Heating on a Modified Clinical Ultrasound Scanner for Generating Mild Hyperthermia in Tumors 
A new system is presented for generating controlled tissue heating with a clinical ultrasound scanner, and initial in vitro and in vivo results are presented that demonstrate both transient and sustained heating in the mild-hyperthermia range of 37–42ºC. The system consists of a Siemens Antares™ ultrasound scanner, a custom dual-frequency 3-row transducer array and an external temperature feedback control system. The transducer has 2 outer rows that operate at 1.5 MHz for tissue heating and a center row that operates at 5 MHz for B-mode imaging to guide the therapy. We compare the field maps obtained using a hydrophone against calculations of the ultrasound beam based on monochromatic and linear assumptions. Using the finite-difference time-domain (FDTD) method, we compare predicted time-dependent thermal profiles to measured profiles for soy tofu as a tissue-mimicking phantom. In vitro results show differential heating of 6ºC for chicken breast and tofu. In vivo tests of the system were performed on three mice bearing Met-1 tumors, which is a model of aggressive, metastatic and highly vascular breast cancer. In superficially implanted tumors, we demonstrate controlled heating to 42ºC. We show that the system is able to maintain the temperature to within 0.1ºC of the desired temperature both in vitro and in vivo.
PMCID: PMC2892277  PMID: 20064754
8.  Comparison of Four Different Shields for Birdcage-Type Coils with Experiments and Numerical Calculations 
Four 12-rung linear birdcage-type coils were built to experimentally examine the effects of the end-ring/shield configuration on radiofrequency magnetic field (B1) homogeneity and SNR at 125 MHz. The coil configurations include (a) a cylindrical shield (conventional), (b) a shield with annular extensions to closely shield the end-rings (surrounding shield), (c) a shield with annular extensions connected to the rungs (solid connection), and (d) a shield with radially oriented conductors connected to the rungs (radial connection). These coils were also modeled closely with finite difference time domain (FDTD) methods to corroborate experimental findings. Images of a human head were acquired, and the signal-to-noise ratio (SNR) was measured on the central axial, sagittal, and coronal slices. B1 field homogeneity in the unloaded coils was assessed on images of an oil phantom. Among the four configurations, the solid connection configuration has a lower SNR than the conventional configuration and the surrounding shield configuration but a higher SNR than the radial connection. Although there is no significant difference between the overall SNR of the conventional configuration and the surrounding shield configuration, the surrounding shield configuration has the potential to be tuned to higher frequencies than the conventional configuration. The conventional birdcage coil results in the most homogeneous B1 field in the oil phantom. Numerical results are also compared with the experimental results.
PMCID: PMC3363294  PMID: 22661912
RF coil; end-ring; B1 homogeneity; SNR; FDTD
9.  Time-multiplexed two-channel capacitive radiofrequency hyperthermia with nanoparticle mediation 
Capacitive radiofrequency (RF) hyperthermia suffers from excessive temperature rise near the electrodes and poorly localized heat transfer to the deep-seated tumor region even though it is known to have potential to cure ill-conditioned tumors. To better localize heat transfer to the deep-seated target region in which electrical conductivity is elevated by nanoparticle mediation, two-channel capacitive RF heating has been tried on a phantom.
We made a tissue-mimicking phantom consisting of two compartments, a tumor-tissue-mimicking insert against uniform background agarose. The tumor-tissue-mimicking insert was made to have higher electrical conductivity than the normal-tissue-mimicking background by applying magnetic nanoparticle suspension to the insert. Two electrode pairs were attached on the phantom surface by equal-angle separation to apply RF electric field to the phantom. To better localize heat transfer to the tumor-tissue-mimicking insert, RF power with a frequency of 26 MHz was delivered to the two channels in a time-multiplexed way. To monitor the temperature rise inside the phantom, MR thermometry was performed at a 3T MRI intermittently during the RF heating. Finite-difference-time-domain (FDTD) electromagnetic and thermal simulations on the phantom model were also performed to verify the experimental results.
As compared to the one-channel RF heating, the two-channel RF heating with time-multiplexed driving improved the spatial localization of heat transfer to the tumor-tissue-mimicking region in both the simulation and experiment. The two-channel RF heating also reduced the temperature rise near the electrodes significantly.
Time-multiplexed two-channel capacitive RF heating has the capability to better localize heat transfer to the nanoparticle-mediated tumor region which has higher electrical conductivity than the background normal tissues.
PMCID: PMC4619487  PMID: 26499058
Capacitive RF hyperthermia; Time-multiplexed RF heating; Nanoparticles; FDTD simulation; MR thermometry
10.  Feasibility of Imaging Tissue Electrical Conductivity by Switching Field Gradients with MRI 
Tissue conductivity is a biophysical marker of tissue structure and physiology. Present methods of measuring tissue conductivity are limited. Electrical impedance tomography, and magnetic resonance electrical impedance tomography rely on passing external current through the object being imaged, which prevents its use in most human imaging. Recently, the RF field used for MR excitation has been used to non-invasively measure tissue conductivity. This technique is promising, but conductivity at higher frequencies is less sensitive to tissue structure. Measuring tissue conductivity non-invasively at low frequencies remains elusive. It has been proposed that eddy currents generated during the rise and decay of gradient pulses could act as a current source to map low-frequency conductivity. This work centers on a gradient echo pulse sequence that uses large gradients prior to excitation to create eddy currents. The electric and magnetic fields during a gradient pulse are simulated by a finite-difference time-domain simulation. The sequence is also tested with a phantom and an animal MRI scanner equipped with gradients of high gradient strengths and slew rate. The simulation demonstrates that eddy currents in materials with conductivity similar to biological tissue decay with a half-life on the order of nanoseconds and any eddy currents generated prior to excitation decay completely before influencing the RF signal. Gradient-induced eddy currents can influence phase accumulation after excitation but the effect is too small to image. The animal scanner images show no measurable phase accumulation. Measuring low-frequency conductivity by gradient-induced eddy currents is presently unfeasible.
PMCID: PMC4734905  PMID: 26844302
Eddy currents; Gradient; MRI; Conductivity; FDTD Simulation
11.  Impact of Indoor Environment on Path Loss in Body Area Networks 
Sensors (Basel, Switzerland)  2014;14(10):19551-19560.
In this paper the influence of an example indoor environment on narrowband radio channel path loss for body area networks operating around 2.4 GHz is investigated using computer simulations and on-site measurements. In contrast to other similar studies, the simulation model included both a numerical human body phantom and its environment—room walls, floor and ceiling. As an example, radio signal attenuation between two different configurations of transceivers with dipole antennas placed in a direct vicinity of a human body (on-body scenario) is analyzed by computer simulations for several types of reflecting environments. In the analyzed case the propagation environments comprised a human body and office room walls. As a reference environment for comparison, free space with only a conducting ground plane, modelling a steel mesh reinforced concrete floor, was chosen. The transmitting and receiving antennas were placed in two on-body configurations chest–back and chest–arm. Path loss vs. frequency simulation results obtained using Finite Difference Time Domain (FDTD) method and a multi-tissue anthropomorphic phantom were compared to results of measurements taken with a vector network analyzer with a human subject located in an average-size empty cuboidal office room. A comparison of path loss values in different environments variants gives some qualitative and quantitative insight into the adequacy of simplified indoor environment model for the indoor body area network channel representation.
PMCID: PMC4239947  PMID: 25333289
Body Area Networks; FDTD; body phantoms; on-body sensor network; wearable antennas
12.  Viable Three-Dimensional Medical Microwave Tomography: Theory and Numerical Experiments 
Three-dimensional microwave tomography represents a potentially very important advance over 2D techniques because it eliminates associated approximations which may lead to more accurate images. However, with the significant increase in problem size, computational efficiency is critical to making 3D microwave imaging viable in practice. In this paper, we present two 3D image reconstruction methods utilizing 3D scalar and vector field modeling strategies, respectively. Finite element (FE) and finite-difference time-domain (FDTD) algorithms are used to model the electromagnetic field interactions in human tissue in 3D. Image reconstruction techniques previously developed for the 2D problem, such as the dual-mesh scheme, iterative block solver, and adjoint Jacobian method are extended directly to 3D reconstructions. Speed improvements achieved by setting an initial field distribution and utilizing an alternating-direction implicit (ADI) FDTD are explored for 3D vector field modeling. The proposed algorithms are tested with simulated data and correctly recovered the position, size and electrical properties of the target. The adjoint formulation and the FDTD method utilizing initial field estimates are found to be significantly more effective in reducing the computation time. Finally, these results also demonstrate that cross-plane measurements are critical for reconstructing 3D profiles of the target.
PMCID: PMC2844097  PMID: 20352084
Adjoint method; alternating-direction implicit finite-difference time-domain (ADI-FDTD); finite-difference time-domain (FDTD); microwave tomography
13.  Comparison of a triaxial fluxgate magnetometer and Toftness sensometer for body surface EMF measurement 
The use of magnetic fields to treat disease has intrigued mankind since the time of the ancient Greeks. More recently it has been shown that electromagnetic field (EMF) treatment aids bone healing, and repetitive transcranial magnetic stimulation (rTMS) appears to be beneficial in treating schizophrenia and depression. Since external EMFs influence internal body processes, we hypothesized that measurement of body surface EMFs might be used to detect disease states and direct the course of subsequent therapy. However, measurement of minute body surface EMFs requires use of a sensitive and well documented magnetometer. In this study we evaluated the sensitivity and frequency response of a fluxgate magnetometer with a triaxial probe for use in detecting body surface EMF and we compared the magnetometer readings with a signal from a Toftness Sensometer, operated by an experienced clinician, in the laboratory and in a clinical setting.
A Peavy Audio Amplifier and variable power output Telulex signal generator were used to develop 50 μT EMFs in a three coil Merritt coil system. A calibrated magnetometer was used to set a 60 Hz 50 μT field in the coil and an ammeter was used to measure the current required to develop the 50 μT field. At frequencies other than 60 Hz, the field strength was maintained at 50 μT by adjusting the Telulex signal output to keep the current constant. The field generated was monitored using a 10 turn coil connected to an oscilloscope. The oscilloscope reading indicated that the field strength was the same at all frequencies tested. To determine if there was a correspondence between the signals detected by a fluxgate magnetometer (FGM1) and the Toftness Sensometer both devices were placed in the Merritt coil and readings were recorded from the FGM1 and compared with the ability of a highly experienced Toftness operator to detect the 50 μT field. Subsequently, in a clinical setting, FGM1 readings made by an FGM1 technician and Sensometer readings were made by 4 Toftness Sensometer operators, having various degrees of experience with this device. Each examiner obtained instrument readings from 5 different volunteers in separate chiropractic adjusting rooms. Additionally, one of the Toftness Sensometers was equipped with an integrated fluxgate magnetometer (FGM2) and this magnetometer was used to obtain a second set of EMF readings in the clinical setting.
The triaxial fluxgate magnetometer was determined to be moderately responsive to changes in magnetic field frequency below 10 Hz. At frequencies above 10 Hz the readings corresponded to that of the ambient static geofield. The practitioner operating the Toftness Sensometer was unable to detect magnetic fields at high frequencies (above 10 Hz) even at very high EMFs. The fluxgate magnetometer was shown to be essentially a DC/static magnetic field detector and like all such devices it has a limited frequency range with some low level of sensitivity at very low field frequencies. The interexaminer reliability of four Toftness practitioners using the Sensometer on 5 patients showed low to moderate correlation.
The fluxgate magnetometer although highly sensitive to static (DC) EMFs has only limited sensitivity to EMFs in the range of 1 to 10 Hz and is very insensitive to frequencies above 10 Hz. In laboratory comparisons of the Sensometer and the fluxgate magnetometer there was an occasional correspondence between the two instruments in detecting magnetic fields within the Merritt coil but these occasions were not reproducible. In the clinical studies there was low to moderate agreement between the clinicians using the Sensometer to diagnosing spinal conditions and there was little if any agreement between the Sensometer and the fluxgate magnetometer in detecting EMFs emanating from the volunteers body surface.
PMCID: PMC1769295  PMID: 17549105
Toftness; Magnetometer; EMF; Chiropractic
14.  Evaluation of a New 1H/31P Dual-Tuned Birdcage Coil for 31P Spectroscopy 
We introduce a new dual-tuned Hydrogen/Phosphorus (1H/31P) birdcage coil, referred to as split birdcage coil, and evaluate its performance using both simulations and magnetic resonance (MR) experiments on a 3 T MR scanner. The proposed coil simplifies the practical matters of tuning and matching, which makes the coil easily reproducible. Simulations were run with the Finite Difference in Time Domain (FDTD) method to evaluate the sensitivity and homogeneity of the magnetic field generated by the proposed 1H coils. Following simulations, MR experiments were conducted using both a phantom and human thigh to compare the proposed design with a currently available commercial dual-tuned flexible surface coil, referred to as flex surface coil, for signal to noise ratio (SNR) as well as homogeneity for the 31P coil. At regions deep within the human thigh, the split birdcage coil was able to acquire spectroscopic signal with a higher average SNR than the flex surface coil. For all regions except those close to the flex surface coil, the split birdcage coil matched or exceeded the performance of the flex surface coil.
PMCID: PMC3770192  PMID: 24039555
Dual-Tuned Birdcage; Spectroscopy; Magnetic Resonance Imaging; Chemical Shift Imaging
15.  Production, detection, storage and release of spin currents 
Background: Quantum rings connected to ballistic circuits couple strongly to external magnetic fields if the connection is not symmetric. Moreover, properly connected rings can be used to pump currents in the wires giving raise to a number of interesting new phenomena. At half filling using a time-dependent magnetic field in the plane of the ring one can pump a pure spin current, excited by the the spin–orbit interaction in the ring.
Results: Such a magnetic current is even under time reversal and produces an electric field instead of the usual magnetic field. Numerical simulations show that one can use magnetizable bodies as storage units to concentrate and save the magnetization in much the same way as capacitors operating with charge currents store electric charge. The polarization obtained in this way can then be used on command to produce spin currents in a wire. These currents show interesting oscillations while the storage units exchange their polarizations.
Conclusion: The magnetic production of spin currents can be a useful alternative to optical excitation and electric field methods.
PMCID: PMC4362210  PMID: 25821714
quantum pumping; quantum transport; spin current
16.  A dual-tuned quadrature volume coil with mixed λ/2 and λ/4 microstrip resonators for multinuclear MRSI at 7T 
Magnetic Resonance Imaging  2011;30(2):290-298.
In this work, an 8-element by 8-element dual-tuned quadrature volume coil with a mix of capacitor terminated half-wavelength (λ/2) and quarter-wavelength (λ/4) microstrip resonators is proposed for multinuclear MRI/S studies at 7T. In the proton channel, λ/2 microstrip resonators with capacitive terminations on both ends are employed for operation at higher frequency of 298.1 MHz; in the heteronucleus channel, capacitor terminated λ/4 resonators, suitable for low frequency operations, are used to meet the low frequency requirement. This mixed structure design is particularly advantageous for high field heteronuclei MR applications with large difference in Larmor frequency of the nuclei in question. The proposed design method makes it much easier to perform frequency tuning for heteronucleus channel using a variable capacitor with a practical capacitance range. As an example, a dual-tuned volume coil for 1H/13C mouse spectroscopic imaging was proposed to demonstrate the feasibility of this method. The finite-difference time-domain (FDTD) method is first used to model this dual-tuned volume coil and calculate the B1 field distributions at two frequencies. Transmission parameters (S21) measured between the proton channel and the carbon channel are −50 dB at 75 MHz and −35 dB at 298 MHz, showing the excellent isolation between the two channels at 7T. The proton image and 13C FID CSI image of a corn oil phantom on the axial plane at 7T demonstrate the feasibility of the proposed method. A preliminary proton image of a mouse on the sagittal plane is also acquired using the proposed dual-tuned volume coil at 7T, illustrating a fairly uniform B1 field and sufficient image coverage for imaging in mice.
PMCID: PMC3254778  PMID: 22055851
Dual-tuned; Microstrip; Volume coil; 7T; mouse imaging; MRI/S
17.  Optimization of magnetic flux density for fast MREIT conductivity imaging using multi-echo interleaved partial fourier acquisitions 
Magnetic resonance electrical impedance tomography (MREIT) has been introduced as a non-invasive method for visualizing the internal conductivity and/or current density of an electrically conductive object by externally injected currents. The injected current through a pair of surface electrodes induces a magnetic flux density distribution inside the imaging object, which results in additional magnetic flux density. To measure the magnetic flux density signal in MREIT, the phase difference approach in an interleaved encoding scheme cancels out the systematic artifacts accumulated in phase signals and also reduces the random noise effect by doubling the measured magnetic flux density signal. For practical applications of in vivo MREIT, it is essential to reduce the scan duration maintaining spatial-resolution and sufficient contrast. In this paper, we optimize the magnetic flux density by using a fast gradient multi-echo MR pulse sequence. To recover the one component of magnetic flux density Bz, we use a coupled partial Fourier acquisitions in the interleaved sense.
To prove the proposed algorithm, we performed numerical simulations using a two-dimensional finite-element model. For a real experiment, we designed a phantom filled with a calibrated saline solution and located a rubber balloon inside the phantom. The rubber balloon was inflated by injecting the same saline solution during the MREIT imaging. We used the multi-echo fast low angle shot (FLASH) MR pulse sequence for MRI scan, which allows the reduction of measuring time without a substantial loss in image quality.
Under the assumption of a priori phase artifact map from a reference scan, we rigorously investigated the convergence ratio of the proposed method, which was closely related with the number of measured phase encode set and the frequency range of the background field inhomogeneity. In the phantom experiment with a partial Fourier acquisition, the total scan time was less than 6 seconds to measure the magnetic flux density Bz data with 128×128 spacial matrix size, where it required 10.24 seconds to fill the complete k-space region.
Numerical simulation and experimental results demonstrated that the proposed method reduces the scanning time and provides the recovered Bz data comparable to what we obtained by measuring complete k-space data.
PMCID: PMC3766253  PMID: 23981409
MREIT; MRI; Interleaved partial fourier acquisition; Magnetic flux density; Current density
18.  A Heterogeneous Nonlinear Attenuating Full-Wave Model of Ultrasound 
A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain (FDTD). Three-dimensional solutions of the equation are verified with water tank measurements of a commercial diagnostic ultrasound transducer and are shown to be in excellent agreement in terms of the fundamental and harmonic acoustic fields and the power spectrum at the focus. The linear and nonlinear components of the algorithm are also verified independently. In the linear nonattenuating regime solutions match results from Field II, a well established software package used in transducer modeling, to within 0.3 dB. Nonlinear plane wave propagation is shown to closely match results from the Galerkin method up to 4 times the fundamental frequency. In addition to thermoviscous attenuation we present a numerical solution of the relaxation attenuation laws that allows modeling of arbitrary frequency dependent attenuation, such as that observed in tissue. A perfectly matched layer (PML) is implemented at the boundaries with a numerical implementation that allows the PML to be used with high-order discretizations. A −78 dB reduction in the reflected amplitude is demonstrated. The numerical algorithm is used to simulate a diagnostic ultrasound pulse propagating through a histologically measured representation of human abdominal wall with spatial variation in the speed of sound, attenuation, nonlinearity, and density. An ultrasound image is created in silico using the same physical and algorithmic process used in an ultrasound scanner: a series of pulses are transmitted through heterogeneous scattering tissue and the received echoes are used in a delay-and-sum beam-forming algorithm to generate a images. The resulting harmonic image exhibits characteristic improvement in lesion boundary definition and contrast when compared with the fundamental image. We demonstrate a mechanism of harmonic image quality improvement by showing that the harmonic point spread function is less sensitive to reverberation clutter.
PMCID: PMC4437716  PMID: 19411208
19.  Polarization Properties in Apertureless-Type Scanning Near-Field Optical Microscopy 
Polarization properties of apertureless-type scanning near-field optical microscopy (a-SNOM) were measured experimentally and were also analyzed using a finite-difference time-domain (FDTD) simulation. Our study reveals that the polarization properties in the a-SNOM are maintained and the a-SNOM works as a wave plate expressed by a Jones matrix. The measured signals obtained by the lock-in detection technique could be decomposed into signals scattered from near-field region and background signals reflected by tip and sample. Polarization images measured by a-SNOM with an angle resolution of 1° are shown. FDTD analysis also reveals the polarization properties of light in the area between a tip and a sample are p-polarization in most of cases.
PMCID: PMC4586183  PMID: 26415540
a-SNOM; Polarization property; FDTD; Jones matrix; 07.79.Fc; 42.25.Ja; 02.70.Bf
20.  Introduction to power-frequency electric and magnetic fields. 
Environmental Health Perspectives  1993;101(Suppl 4):73-81.
This paper introduces the reader to electric and magnetic fields, particularly those fields produced by electric power systems and other sources using frequencies in the power-frequency range. Electric fields are produced by electric charges; a magnetic field also is produced if these charges are in motion. Electric fields exert forces on other charges; if in motion, these charges will experience magnetic forces. Power-frequency electric and magnetic fields induce electric currents in conducting bodies such as living organisms. The current density vector is used to describe the distribution of current within a body. The surface of the human body is an excellent shield for power-frequency electric fields, but power-frequency magnetic fields penetrate without significant attenuation; the electric fields induced inside the body by either exposure are comparable in magnitude. Electric fields induced inside a human by most environmental electric and magnetic fields appear to be small in magnitude compared to levels naturally occurring in living tissues. Detection of such fields thus would seem to require the existence of unknown biological mechanisms. Complete characterization of a power-frequency field requires measurement of the magnitudes and electrical phases of the fundamental and harmonic amplitudes of its three vector components. Most available instrumentation measures only a small subset, or some weighted average, of these quantities. Hand-held survey meters have been used widely to measure power-frequency electric and magnetic fields. Automated data-acquisition systems have come into use more recently to make electric- and magnetic-field recordings, covering periods of hours to days, in residences and other environments.(ABSTRACT TRUNCATED AT 250 WORDS)
PMCID: PMC1519708  PMID: 8206045
21.  The Global Coherence Initiative: Creating a Coherent Planetary Standing Wave 
The much anticipated year of 2012 is now here. Amidst the predictions and cosmic alignments that many are aware of, one thing is for sure: it will be an interesting and exciting year as the speed of change continues to increase, bringing both chaos and great opportunity. One benchmark of these times is a shift in many people from a paradigm of competition to one of greater cooperation. All across the planet, increasing numbers of people are practicing heart-based living, and more groups are forming activities that support positive change and creative solutions for manifesting a better world. The Global Coherence Initiative (GCI) is a science-based, co-creative project to unite people in heart-focused care and intention. GCI is working in concert with other initiatives to realize the increased power of collective intention and consciousness.
The convergence of several independent lines of evidence provides strong support for the existence of a global information field that connects all living systems and consciousness. Every cell in our bodies is bathed in an external and internal environment of fluctuating invisible magnetic forces that can affect virtually every cell and circuit in biological systems. Therefore, it should not be surprising that numerous physiological rhythms in humans and global collective behaviors are not only synchronized with solar and geomagnetic activity, but disruptions in these fields can create adverse effects on human health and behavior.
The most likely mechanism for explaining how solar and geomagnetic influences affect human health and behavior are a coupling between the human nervous system and resonating geomagnetic frequencies, called Schumann resonances, which occur in the earth-ionosphere resonant cavity and Alfvén waves. It is well established that these resonant frequencies directly overlap with those of the human brain and cardiovascular system. If all living systems are indeed interconnected and communicate with each other via biological, electromagnetic, and nonlocal fields, it stands to reason that humans can work together in a co-creative relationship to consciously increase the coherence in the global field environment, which in turn distributes this information to all living systems within the field.
GCI was established to help facilitate the shift in global consciousness from instability and discord to balance, cooperation, and enduring peace. A primary goal of GCI is to test the hypothesis that large numbers of people when in a heart-coherent state and holding a shared intention can encode information on the earth's energetic and geomagnetic fields, which act as carrier waves of this physiologically patterned and relevant information. In order to conduct this research, a global network of 12 to 14 ultrasensitive magnetic field detectors specifically designed to measure the earth's magnetic resonances is being installed strategically around the planet. More important is GCI's primary goal to motivate as many people as possible to work together in a more coherent and collaborative manner to increase the collective human consciousness.
If we are persuaded that not only external fields of solar and cosmic origins but also human attention and emotion can directly affect the physical world and the mental and emotional states of others (consciousness), it broadens our view of what interconnectedness means and how it can be intentionally utilized to shape the future of the world we live in. It implies that our attitudes, emotions, and intentions matter and that coherent, cooperative intent can have positive effects.
GCI hypothesizes that when enough individuals and social groups increase their coherence baseline and utilize that increased coherence to intentionally create a more coherent standing reference wave in the global field, it will help increase global consciousness. This can be achieved when an increasing number of people move towards more balanced and self-regulated emotions and responses. This in turn can help facilitate cooperation and collaboration in innovative problem solving and intuitive discernment for addressing society's significant social, environmental, and economic problems. In time, as more individuals stabilize the global field and families, workplaces, and communities move to increased social coherence, it will lead to increased global coherence. This will be indicated by countries adopting a more coherent planetary view so that social and economic oppression, warfare, cultural intolerance, crime, and disregard for the environment can be addressed meaningfully and successfully.
PMCID: PMC3833489  PMID: 24278803
Global Coherence Initiative; geomagnetic; Schumann resonances; coherence; heart-based living; global health
22.  Rapid computation of the amplitude and phase of tightly focused optical fields distorted by scattering particles 
We develop an efficient method for accurately calculating the electric field of tightly focused laser beams in the presence of specific configurations of microscopic scatterers. This Huygens–Fresnel wave-based electric field superposition (HF-WEFS) method computes the amplitude and phase of the scattered electric field in excellent agreement with finite difference time-domain (FDTD) solutions of Maxwell’s equations. Our HF-WEFS implementation is 2–4 orders of magnitude faster than the FDTD method and enables systematic investigations of the effects of scatterer size and configuration on the focal field. We demonstrate the power of the new HF-WEFS approach by mapping several metrics of focal field distortion as a function of scatterer position. This analysis shows that the maximum focal field distortion occurs for single scatterers placed below the focal plane with an offset from the optical axis. The HF-WEFS method represents an important first step toward the development of a computational model of laser-scanning microscopy of thick cellular/tissue specimens.
PMCID: PMC4213127  PMID: 25121440
23.  Iterative multi-channel radio frequency pulse calibration with improving B1 field uniformity in high field MRI 
In high field MRI capable of multi-channel radio frequency (RF) transmission, B1 shimming is a time-consuming job because conventional B1 shimming techniques require B1 mapping for each channel. After acquiring the complex-numbered B1 field maps, the optimal amplitude and phase of the driving RF pulse are determined for each channel to maximize the B1 field uniformity in conventional B1 shimming. However, time-consuming B1 shimming procedures at the pre-scan may not be tolerated in the clinical imaging in which patient throughput is one of the important factors.
To avoid the time-consuming B1 mapping, the first spin echo and the stimulated echo were repeatedly acquired in the slice-selective stimulated echo sequence without imaging gradients. A cost function of the amplitudes and phases of the driving RF pulse for every channel was defined in a way that the ratio between the spin echo and stimulated echo amplitudes rapidly converged to √ 2. The amplitude and phase of the driving RF pulse were iteratively modified over the repeating RF pulse sequence so that the cost function was minimized.
From the finite-difference-time-domain (FDTD) electromagnetic field simulations with a human body model placed in a birdcage coil operating at 3 T, it was observed that the RF pulse calibration with iterative cost function minimization can give improvement of B1 field uniformity as well as flip-angle calibration. The experiments at 3 T also showed improvement of RF field uniformity in the phantom imaging studies.
Since the proposed RF pulse calibration is not based on B1 mapping, the RF pulse calibration time could be much shorter than the B1-mapping based methods. The proposed method is expected to be a practical substitute for the B1-mapping-based B1 shimming methods when long pre-scan time is not tolerable.
PMCID: PMC4340295  PMID: 25884219
RF pulse calibration; MRI; B1 uniformity; B1 mapping; B1 shimming
24.  Reconstruction of dual-frequency conductivity by optimization of phase map in MREIT and MREPT 
The spectroscopic conductivity distribution of tissue can help to explain physiological and pathological status. Dual frequency conductivity imaging by combining Magnetic Resonance Electrical Property Tomography (MREPT) and Magnetic Resonance Electrical Impedance Tomography (MREIT) has been recently proposed. MREIT can provide internal conductivity distributions at low frequency (below 1 kHz) induced by an external injecting current. While MREPT can provide conductivity at the Larmor frequency related to the strength of the magnetic field. Despite this potential to describe the membrane properties using spectral information, MREPT and MREIT techniques currently suffer from weak signals and noise amplification as they both reply on differentiation of measured phase data.
We proposed a method to optimize the measured phase signal by finding weighting factors according to the echo signal for MREPT and MREIT using the ICNE (Injected current nonlinear encoding) multi-echo pulse sequence. Our target weights are chosen to minimize the measured noise. The noise standard deviations were precisely analyzed for the optimally weighted magnetic flux density and the phase term of the positive-rotating magnetic field. To enhance the quality of dual-frequency conductivity images, we applied the denoising method based on the reaction-diffusion equation with the estimated noise standard deviations. A real experiment was performed with a hollow cylindrical object made of thin insulating film with holes to control the apparent conductivity using ion mobility and an agarose gel cylinder wrapped in an insulating film without holes to show different spectroscopic conductivities.
The ability to image different conductivity characteristics in MREPT and MREIT from a single MR scan was shown by including the two objects with different spectroscopic conductivities. Using the six echo signals, we computed the optimized weighting factors for each echo. The qualities of conductivity images for MREPT and MREIT were improved by optimization of the phase map. The proposed method effectively reduced the random noise artifacts for both MREIT and MREPT.
We enhanced the dual conductivity images using the optimally weighted magnetic flux density and the phase term of positive-rotating magnetic field based on the analysis of the noise standard deviations and applying the optimization and denoising methods.
PMCID: PMC3995946  PMID: 24607262
MRI; MREIT; MREPT; Conductivity; Magnetic flux density; Optimization
25.  Finite volume analysis of temperature effects induced by active MRI implants: 2. Defects on active MRI implants causing hot spots 
Active magnetic resonance imaging implants, for example stents, stent grafts or vena cava filters, are constructed as wireless inductively coupled transmit and receive coils. They are built as a resonator tuned to the Larmor frequency of a magnetic resonance system. The resonator can be added to or incorporated within the implant. This technology can counteract the shielding caused by eddy currents inside the metallic implant structure. This may allow getting diagnostic information of the implant lumen (in stent stenosis or thrombosis for example). The electro magnetic rf-pulses during magnetic resonance imaging induce a current in the circuit path of the resonator. A by material fatigue provoked partial rupture of the circuit path or a broken wire with touching surfaces can set up a relatively high resistance on a very short distance, which may behave as a point-like power source, a hot spot, inside the body part the resonator is implanted to. This local power loss inside a small volume can reach ¼ of the total power loss of the intact resonating circuit, which itself is proportional to the product of the resonator volume and the quality factor and depends as well from the orientation of the resonator with respect to the main magnetic field and the imaging sequence the resonator is exposed to.
First an analytical solution of a hot spot for thermal equilibrium is described. This analytical solution with a definite hot spot power loss represents the worst case scenario for thermal equilibrium inside a homogeneous medium without cooling effects. Starting with this worst case assumptions additional conditions are considered in a numerical simulation, which are more realistic and may make the results less critical. The analytical solution as well as the numerical simulations use the experimental experience of the maximum hot spot power loss of implanted resonators with a definite volume during magnetic resonance imaging investigations. The finite volume analysis calculates the time developing temperature maps for the model of a broken linear metallic wire embedded in tissue. Half of the total hot spot power loss is assumed to diffuse into both wire parts at the location of a defect. The energy is distributed from there by heat conduction. Additionally the effect of blood perfusion and blood flow is respected in some simulations because the simultaneous appearance of all worst case conditions, especially the absence of blood perfusion and blood flow near the hot spot, is very unlikely for vessel implants.
The analytical solution as worst case scenario as well as the finite volume analysis for near worst case situations show not negligible volumes with critical temperature increases for part of the modeled hot spot situations. MR investigations with a high rf-pulse density lasting below a minute can establish volumes of several cubic millimeters with temperature increases high enough to start cell destruction. Longer exposure times can involve volumes larger than 100 mm3. Even temperature increases in the range of thermal ablation are reached for substantial volumes. MR sequence exposure time and hot spot power loss are the primary factors influencing the volume with critical temperature increases. Wire radius, wire material as well as the physiological parameters blood perfusion and blood flow inside larger vessels reduce the volume with critical temperature increases, but do not exclude a volume with critical tissue heating for resonators with a large product of resonator volume and quality factor.
The worst case scenario assumes thermal equilibrium for a hot spot embedded in homogeneous tissue without any cooling due to blood perfusion or flow. The finite volume analysis can calculate the results for near and not close to worst case conditions. For both cases a substantial volume can reach a critical temperature increase in a short time. The analytical solution, as absolute worst case, points out that resonators with a small product of inductance volume and quality factor (Q Vind < 2 cm3) are definitely save. Stents for coronary vessels or resonators used as tracking devices for interventional procedures therefore have no risk of high temperature increases. The finite volume analysis shows for sure that also conditions not close to the worst case reach physiologically critical temperature increases for implants with a large product of inductance volume and quality factor (Q Vind > 10 cm3). Such resonators exclude patients from exactly the MRI investigation these devices are made for.
PMCID: PMC1513583  PMID: 16729878

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